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Scientific Scientific NotationNotation

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Standard form / Scientific Notation

Scientific Notation very small numbers

Scientific Notation to Number Form

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Starter QuestionsStarter Questionsw

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2. Calculate (- 14)+(- 5)+8

3. What fraction is x:

4. Simplify the fraction

5. Calculate 20% of 210

1680

X

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1.1. To understand and use To understand and use the quick method to put the quick method to put large numbers into large numbers into scientific notation.scientific notation.

1. To show a very quick way of putting a large number in scientific notation very quickly.

Scientific Notation

Very large numbers!

BOOM!

How far?

92 000 000 miles

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How many seconds in 70 years?

70 years = 2 200 000 000 seconds!

Very large numbers!Happy 70th Birthday!

SPLAT!

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Dinosaurs roamed the earth 228 million years

ago

Very large numbers!

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Short hand !

100 = 10 x 10

1 000 = 10 x 10 x 10

100 000 = 10 x 10 x 10 x 10 x 10

10 000 = 10 x 10 x 10 x 10

1 000 000 = 10 x 10 x 10 x 10 x 10 x 10

10 210

310410

510

110

610

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Standard Form

200 = 2 x 100

4 000 = 4 x 1000

500 000 = 5 x 100 000

70 000 = 7 x 10 000

3 000 000 = 3 x 1 000 000

22 10 34 10 47 10 55 10 63 10

This is also known as

Scientific Notation.

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Standard FormExercise 1

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(1)2 000

(2) 20 000

(3) 500

(4) 800 000

(5) 9 000 000

= 5 x 100 25 10

= 8 x 100 000 58 10

= 2 x 10 000 42 10

= 9 x 1 000 000 69 10

= 2 x 1000 32 10

Add the decimal point

A short cut

8 000 000 68 10 ..

Between 1 and 10

The point moved 6 places

Move the point to get a number between 1 and 10

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92 000 000 79.2 10 ..

Add the decimal point

Between 1 and 10

The point moved 7 places

Move the point to get a number between 1 and 10

79.2 10 miles

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A short cut

2 200 000 000 92.2 10 ..

Add the decimal point

Between 1 and 10

The point moved 9 places

Move the point to get a number between 1 and 10

Happy Birthday: Seconds old! 92.2 10

A short cut

228 000 000 82.28 10 ..

Add the decimal point

Between 1 and 10

The point moved 8 places

Move the point to get a number between 1 and 10

82.28 10 years ago!ww

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A short cut

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Standard Form

(1) 30 000(2) 700 000(3) 5 300(4) 470 000(5) 9 500 000(6) 18 300 000(7) 329 000(8) 2 560 000(9) 12 000 000 000(10) 9 990 000

35.3 10 54.7 10

57 10

69.5 10

43 10

71.83 10 53.29 10 62.56 10

101.2 10 69.99 10

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Starter QuestionsStarter Questionsw

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2 3 5 4 5y x y x xy

1. Find the highest number that divides into 8 and 18 without leaving a remainder.

2. Simplify

3. Write 72% as a decimal

4. Write in scientific notation 230000

5. 30% of £600

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Scientific Scientific NotationNotation

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1.1. Know how to expand Know how to expand large numbers in large numbers in scientific notation to scientific notation to number format.number format.

1. To understand how to change large numbers from Scientific Notation to number form.

=86 000 000 78.6 10

Zeros after the point aren’t needed.

The point moves 7 places

8.60000000.

Hint:Add 7 zeros, although

you probably won’t need them all.

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Changing back

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=346 00053.46 10

Zeros after the point aren’t needed.

The point moves 5 places

3.4600000.Hint:

Add 5 zeros, although you probably won’t need

them all.

Changing back

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Changing back

(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)

56.5 1081.2 10

38 10

63.71 10

56 10

43.3 1067.91 1075.55 1041.05 1093.033 10

= 600 000= 8 000= 650 000= 120 000 000= 3 710 000= 33 000= 7 910 000= 55 500 000= 10 500= 3 033 000 000

Name that number!

10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000

1001 10

1 000

1 000 000

1 000 000 000

31 10 61 10 91 10

one thousand

one million

one billion

one googal !!!

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Starter QuestionsStarter Questionsw

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6 9 15 14 5a b a b a

1. Find the highest number that divises into 28 and 14 without leaving a renainder.

2. Simplify

3. Write 55% as a decimal

4. Find the lowest number that both of 5 and 9 divide into without leaving a remainder.

5. 15% of £400

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Scientific Scientific NotationNotation

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1.1. Know how to change Know how to change very small numbers into very small numbers into scientific notation and scientific notation and how to do the reverse how to do the reverse process.process.

1. To understand how to change very small numbers into Scientific Notation and vice versa.

Very small numbers!

How wide is an atom?

0.000 000 000 1 metres wide!

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0.000 000 000 1

101 10 .

The point moved 10 places. Negative sign for small numbers.

Move the point to get a number between 1 and 10

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Standard Form for small numbers

0.000 000 76 77.6 10 .

The point moved 7 places. Negative sign for small numbers.

Move the point to get a number between 1 and 10

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Standard Form for small numbers

Standard Form for small numbers

0.000 001 93 61.93 10 .

The point moved 6 places. Negative sign for small numbers.

Move the point to get a number between 1 and 10

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Standard Form for small numbers

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(2) 0.000 07(3) 0.000 45(4) 0.003 4(5) 0. 000 724(6) 0.000 000 494(7) 0.000 095(8) 0.000 000 098(9) 0.000 1 03(10) 0.000 000 000 66

44.5 10 33.4 10

57 10

47.24 10

43 10

74.94 10 59.5 10 89.8 10 41.03 10 106.6 10

= 0.002

-32 10 2000.

Hint:Add 3 zeros to the left of

the number.

-3 so remember to move point left for small numbers.

.

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Changing back small numbers

= 0.000 086

-58.6 10 8.600000.

Hint:Add 5 zeros to the left of

the number.

-5 so remember to move point left for small numbers.

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Changing back small numbers

Changing back small numbers

= 0.000 00516

-65.16 10 5.16000000.

Hint:Add 6 zeros to the left of

the number.

-6 so remember to move point left for small numbers.

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(2)(3)(4)(5)(6)(7)(8)(9)(10)

35.8 1076.2 10

59 10

66.45 10

45 10

75.3 1069.17 1032.12 1052.03 1096.032 10

= 0.000 5= 0.000 09= 0.005 8= 0.000 000 62= 0.000 006 45= 0.000 000 53= 0.000 009 17= 0.002 12= 0.000 020 3= 0.000 000 006 032

Changing back small numbers